Question

# A factorial experiment was designed to test for any significant differences in the time needed to...

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

 Language Spanish French German System 1 9 12 10 13 16 14 System 2 5 18 15 9 20 21

Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use  = .05.

a. Complete the following ANOVA table (to 2 decimals, if necessary). Round p-value to four decimal places.

 Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Factor A Factor B Interaction Error Total

b. The p-value for Factor A is Select

less than .005

between .005 and .0125

between .0125 and .025

between .025 and .0

greater than .05

What is your conclusion with respect to Factor A?
Factor A is significant

Factor A is not significant

C. The p-value for Factor B is Select

less than .005

between .005 and .0125

between .0125 and .025

between .025 and .05

greater than .05

What is your conclusion with respect to Factor B?
Factor B is significant

Factor B is not significant

D. The p-value for the interaction of factors A and B is Select

less than .005between .005 and .0125

between .0125 and .025

between .025 and .05

greater than .05

What is your conclusion with respect to the interaction of Factors A and B?
Select

The interaction of factors A and B is significant

The interaction of factors A and B is not significant

 Source of Variation SS df MS F P-value factor A 16.33 1 16.33 1.88 0.2189 factor B 126.00 2 63.00 7.27 0.0249 Interaction 60.67 2 30.33 3.50 0.0983 Within 52 6 8.67 Total 255 11

The p-value for Factor A is greater than .05

conclusion with respect to Factor A? : Factor A is not significant

The p-value for Factor B is between .0125 and .025

conclusion with respect to Factor B? : Factor B is significant

p-value for the interaction of factors A and B is greater than .05

conclusion with respect to the interaction of Factors A and B? The interaction of factors A and B is not significant

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